Large deviations on the boundary of and outside the Cramér zone for random walks with jump distributions decaying exponentially fast

2010 ◽  
pp. 300-334
Author(s):  
A. A. Borovkov ◽  
K. A. Borovkov
Keyword(s):  
Large Deviations ◽  
Random Walks

scholarly journals Large deviations of convex hulls of self-avoiding random walks

2018 ◽  
Vol 97 (6) ◽  
Author(s):  
Hendrik Schawe ◽  
Alexander K. Hartmann ◽  
Satya N. Majumdar
Keyword(s):  
Large Deviations ◽  
Random Walks ◽  
Convex Hulls

scholarly journals Asymptotics for the First Passage Times of Lévy Processes and Random Walks

2013 ◽  
Vol 50 (1) ◽  
pp. 64-84 ◽  
Author(s):  
Denis Denisov ◽  
Vsevolod Shneer
Keyword(s):  
Large Deviations ◽  
Random Walks ◽  
Levy Processes ◽  
Levy Process ◽  
First Passage Times ◽  
Exact Asymptotics ◽  
First Passage ◽  
Heavy Tailed ◽  
First Time ◽  
Passage Times

We study the exact asymptotics for the distribution of the first time, τx, a Lévy process Xt crosses a fixed negative level -x. We prove that ℙ{τx >t} ~V(x) ℙ{Xt≥0}/t as t→∞ for a certain function V(x). Using known results for the large deviations of random walks, we obtain asymptotics for ℙ{τx>t} explicitly in both light- and heavy-tailed cases.

scholarly journals Quenched Free Energy and Large Deviations for Random Walks in Random Potentials

2012 ◽  
Vol 66 (2) ◽  
pp. 202-244 ◽  
Author(s):  
Firas Rassoul-Agha ◽  
Timo Seppäläinen ◽  
Atilla Yilmaz
Keyword(s):  
Free Energy ◽  
Large Deviations ◽  
Random Walks ◽  
Random Potentials

scholarly journals Sample path large deviations for Lévy processes and random walks with Weibull increments

2020 ◽  
Vol 30 (6) ◽  
pp. 2695-2739
Author(s):  
Mihail Bazhba ◽  
Jose Blanchet ◽  
Chang-Han Rhee ◽  
Bert Zwart
Keyword(s):  
Large Deviations ◽  
Random Walks ◽  
Lévy Processes ◽  
Sample Path ◽  
Levy Processes ◽  
Sample Path Large Deviations

scholarly journals Large deviations of convex hulls of planar random walks and Brownian motions

2021 ◽  
Vol 4 ◽  
pp. 1163-1201
Author(s):  
Arseniy Akopyan ◽  
Vladislav Vysotsky
Keyword(s):  
Large Deviations ◽  
Random Walks ◽  
Convex Hulls ◽  
Brownian Motions
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